1. Field of the Invention
The present invention relates generally to computer aided ballistic analysis systems and methods and, more particularly, to a computerized ballistic analysis system and methods in which correlation coefficients obtained by comparing land impression data from the surfaces of bullets is statistically analyzed to evaluate gun identifiability and/or bullet-to-gun classifications.
2. Brief Description of the Related Art
The scratches or striations formed on the surface of a bullet by a gun barrel through which the bullet is fired create a signature with enough unique features that it may be matched with other bullets fired by the same gun. The matching process has been manually accomplished for many years using an optical instrument called a comparison microscope. Manual comparisons of bullets can be quite time consuming and such technique is used sparingly unless there is some reason to believe that a bullet from a crime scene was in fact fired from a gun in question.
Recent machines have been built which attempt to automate the process of ballistics analysis. The goal is to enter bullet images into a database and to allow a computer to search the database for matches. Due to the fact that a computer can make such comparisons many times faster than a human, searching large databases is, at least in principle, feasible. The digitized images of bullets and cartridge cases can also be used to provide additional tools which assist firearms examiners in their manual comparisons.
For example, U.S. Pat. No. 5,654,801 to Baldur describes a fired cartridge illumination method and imaging apparatus which includes a light source and a microscope to image impressions on the surface of the cartridge. Images of the impressions are then used for comparative analysis, during which a first image from a test cartridge and a second image from a computer databank are compared with each other and a maximum correlation value between the first and second images is obtained.
As is common among the current systems capturing data from bullets and cartridges, the devices described in the Baldur patent and in U.S. Pat. No. 5,390,108 to Baldur et al capture strictly visual data which does not distinguish between shallow scratches or deep scratches on the surface of the examined cartridge or bullet. Therefore, important analysis parameters are not considered, which lessens matching reliability and reduces provability of consistent conclusions.
A fundamental problem of all computer aided ballistic analysis systems is that bullets fired from the same gun do not match exactly for a number of reasons, including the facts that the cartridge casing may have different amounts of powder, or that the gun barrel may have been at different temperatures when bullets are fired as compared to the test firing. Due to the fact that the impressions made by a gun on a bullet can differ from firing to firing, all comparison algorithms must necessarily be statistical and cannot look for an exact or even nearly exact match of all striations on the bullet""s surface.
Currently, the algorithms which compare bullets have a high false positive match rate. Qualitatively, this means that automatic searching of a large database of ballistic data which may have tens of thousands of entries is not viable. By using the large database, there would be so many false positive matches requiring so many comparisons that essentially no useful information would be obtained. Another problem of current algorithms used in ballistic analysis involves the false negative match rate, resulting in reliable evidence being missed.
The poor false match rate using current algorithms is the result of fundamental problems, most of which are associated with the fact that the data used for the bullet comparisons is 2-D data as represented by the Baldur and Baldur et al patents. 3-D data is much more reliable and robust than 2-D data. In 2-D data capture, a source of light is directed at the bullet""s surface, and a camera records the light as it is reflected by that surface. The data capture process is based on the fact that the light reflected by the bullet""s surface is a function of its surface features. However, this is an indirect measurement because it involves a transformation of the incident light into the light recorded by the camera. By comparison, a 3-D acquisition process is simply the distance between the surface features and an imaginary plane, and is thus a direct measurement. The disadvantages associated with the indirectness of 2-D data capture are:
Robustness: A significant problem associated with 2-D data capture lies in the fact that the transformation relating the light incident on the bullet""s surface and the light reflected by it depends not only on the features of the bullet""s surface, but also on a number of independent parameters such as the angle of incidence of the light, the angle of view of the camera, variations on the reflectivity of the bullet""s surface, light intensity, et cetera. This implies that the captured data (the data recorded by the camera) is also dependent on these parameters. To attempt to eliminate the effect of these parameters on the captured data would be next to impossible, except possibly for light intensity. As a consequence, the 2-D captured data is vulnerable to considerable variability or, in other terms, it is non-robust.
Indeterminate conditions: A different kind of problem associated with 2-D data capture is the presence of indeterminate conditions in the data. Given an incident light source angle, some of the smaller surface features can be xe2x80x9cshadowedxe2x80x9d by the larger features. This implies that there will be regions of the surface where the captured data will not accurately reflect the surface features. In mathematical terms, the transformation between the incident light and the reflected light is non-invertible. Furthermore, this is an example where the angle of incidence of the light source can have a critical effect on the captured data, because arbitrarily small changes in the angle of incidence may determine whether smaller features are detected or not. In mathematical terms, the transformation between the incident light and the reflected light is discontinuous with respect to the angle of incidence.
In summary, 2-D data capture methodologies can be affected by extraneous variables that can be next to impossible to control. Moreover, because these variables are not measured, their effects on the captured data cannot be compensated for. As a consequence, the normalized data resulting from some capture processes is also vulnerable to significant variability or, in other words, lack of repeatability. The performance of even the most sophisticated correlation algorithms will be degraded in the presence of non-repeatable data. Taking in consideration that the bullet matching problem is quite demanding to begin with, it is not surprising that ballistic matching methodologies based on 2-D captured data have had significant difficulties delivering satisfactory performance.
Accordingly, it is a primary object of the present invention to overcome the disadvantages of prior ballistic analysis systems and methods and, in particular, prior computer aided ballistic analysis systems and methods.
Another object of the present invention is to perform ballistic analysis utilizing 3-D information of a bullet""s surface.
A further object of the present invention is to perform ballistic analysis by comparing at least the land impressions of two or more bullets and, in particular, by comparing fine details within the land impressions.
An additional object of the present invention is to determine whether a gun is identifiable utilizing matching coefficients and non-matching coefficients obtained by comparing the land impressions of a plurality of control bullets fired by the gun.
It is also an object of the present invention to utilize matching coefficients, obtained by comparing the land impressions of a plurality of control bullets fired by a gun, and questioned coefficients, obtained by comparing the land impressions of an evidence bullet to the land impressions of the control bullets, to classify the evidence bullet as a match or non-match with the suspect gun.
The present invention has as another object to perform gun identifiability by evaluating the statistical similarity between a set of control bullet matching coefficients and a set of non-matching coefficients.
Yet a further object of the present invention is to evaluate gun identifiability by calculating the similarity between the probability distributions of a set of matching coefficients for control bullets fired by the gun and a set of non-matching coefficients.
Moreover, it is an object of the present invention to classify a bullet in relation to a suspect gun by evaluating the statistical similarity between a set of control bullet matching coefficients and a set of questioned coefficients.
The present invention has as an additional object to classify a bullet in relation to a suspect gun by evaluating the statistical similarity between a set of control bullet matching coefficients and a set of non-matching coefficients.
It is an additional object of the present invention to utilize either different-gun coefficients or same-gun non-matching coefficients as non-matching coefficients in ballistic analysis.
The present invention has as an additional object to estimate the probabilities of error in computerized ballistic analysis.
Some of the advantages of the present invention are that time consuming, manual comparisons of bullets by firearms examiners can be replaced with an automated procedure for gun identifiability and/or bullet-to-gun classifications; conventional statistical tests can be used in the system and methods of the present invention; various algorithms or other mathematical operations can be used in the present invention to compute correlation coefficients for land-to-land comparisons between bullets; ballistic analysis can be performed using only land-to-land comparisons between bullets; ballistic analysis can be performed using groove impression comparisons and/or other bullet impression comparisons in addition to land impression comparisons; human subjectivity and error are eliminated from ballistic analysis; the databases used in the system and methods of the present invention can store land impression data and correlation coefficients for a great number of different bullets to provide a reference database from which specific land impression data and/or correlation coefficients may be accessed on demand; ballistic analysis may be simplified by using same-gun non-matching coefficients as a substitute for different-gun coefficients; although the use of 3-D depth profiles is preferred, 2-D data of the surfaces of bullets can be used in the present invention; any number of control bullets greater than one can be used in the present invention; and various methodology can be used to identify the matching coefficients, the non-matching coefficients and the questioned coefficients.
These and other objects, advantages and benefits are realized with the present invention as generally characterized in a computerized system for ballistic analysis comprising a data acquisition unit for acquiring data of a bullet""s surface and, in particular, land impression data of a bullet""s surface, and a data processor having software for statistically comparing land impression data of the surfaces of a plurality of bullets to one another. To evaluate the identifiability of a suspect gun, the data processor compares land impression data of the surfaces of a plurality of control bullets, fired by the suspect gun, to one another in all possible relative orientations for the control bullets. The data processor computes a correlation coefficient for each land-to-land comparison between the control bullets and identifies a set of matching coefficients for the control bullets corresponding to the correlation coefficients in which each pair of the control bullets is in a relative orientation of greatest match. The data processor also identifies a set of non-matching coefficients, which may comprise a set of same-gun non-matching coefficients for the control bullets or a set of different-gun coefficients. The data processor statistically evaluates whether or not the sets of matching coefficients and non-matching coefficients are statistically indistinguishable, and a Rank-Sum test may be used for the statistical evaluation. The data processor concludes the suspect gun as being identifiable in response to a statistical evaluation that the sets of matching coefficients and non-matching coefficients are not statistically undistinguishable.
The computerized system for ballistic analysis may be used to classify an evidence bullet with respect to a suspect gun, and the data processor includes software for comparing land impression data of the surface of at least one evidence bullet with land impression data of the surfaces of a plurality of control bullets in all possible relative orientations for the evidence bullet and the control bullets. The data processor computes a correlation coefficient for each land-to-land comparison between the evidence bullet and the control bullets, respectively, and identifies a set of questioned coefficients for the evidence bullet and the control bullets. The data processor statistically evaluates whether or not a set of matching coefficients for the control bullets is statistically equivalent to the set of questioned coefficients. The data processor concludes that the evidence bullet was fired by the suspect gun in response to a statistical evaluation that the sets of matching coefficients and questioned coefficients are statistically equivalent. A set of non-matching coefficients, either same-gun non-matching coefficients for the control bullets or different-gun coefficients, may be statistically evaluated by the data processor for statistical equivalence to the set of questioned coefficients, and the data processor concludes that the evidence bullet was not fired by the suspect gun in response to a statistical evaluation that the sets of non-matching coefficients and questioned coefficients are statistically equivalent.
In the computerized system for ballistic analysis of the present invention, 3-D depth profiles are preferably used for the land-to-land comparisons, including fine details within the land impressions. The system may include a filter or other means for isolating features of the land impressions within intermediate length scales. In addition, the system may include normalization software for compensating the acquired depth profiles for various measurement errors. Various correlation algorithms or other mathematical functions or operations may be used in the computerized system for ballistic analysis to calculate the correlation coefficients as a quantitative measure of the similarity of the land impressions under comparison. Various methodologies may be used to identify the matching coefficients, the non-matching coefficients and the different-gun coefficients.
A method of computerized ballistic analysis in accordance with the present invention comprises the steps of comparing land impressions on the surfaces of a plurality of control bullets, fired by a suspect gun, to one another in all possible relative orientations for the control bullets and computing a correlation coefficient for each land-to-land comparison. A set of matching coefficients is identified corresponding to the correlation coefficients in which each pair of the control bullets is in a relative orientation of greatest match. A set of non-matching coefficients is identified and may involve identifying a set of different-gun coefficients obtained by comparing the land impressions of a plurality of bullets fired by different guns of the same model as the suspect gun or a set of same-gun non-matching coefficients corresponding to the correlation coefficients in which each pair of the control bullets is in a non-matching relative orientation of less than greatest match. The method further comprises statistically evaluating whether or not the sets of matching coefficients and non-matching coefficients are statistically undistinguishable and concluding the suspect gun is identifiable in response to a statistical evaluation that the sets of matching coefficients and non-matching coefficients are not statistically undistinguishable.
Another method of the present invention involves comparing land impressions on the surface of at least one evidence bullet with the land impressions on each of a plurality of control bullets, fired by a suspect gun, in all possible relative orientations between the evidence bullet and the control bullets, computing a correlation coefficient for each land-to-land comparison between the evidence bullet and the control bullets, respectively, and identifying a set of questioned coefficients for the evidence bullet and the control bullets. A set of matching coefficients for the control bullets is statistically evaluated with the set of questioned coefficients to determine whether or not the set of matching coefficients is statistically equivalent to the set of questioned coefficients. Where the statistical evaluation presents the sets of matching coefficients and questioned coefficients as being statistically equivalent, it is concluded that the evidence bullet was fired by the suspect gun. The method of the present invention may further include statistically evaluating whether or not a set of non-matching coefficients, either different-gun coefficients or same-gun non-matching coefficients, is statistically equivalent to the set of questioned coefficients and concluding the evidence bullet was not fired by the suspect gun in response to a statistical evaluation that the sets of non-matching coefficients and questioned coefficients are statistically equivalent. Various numbers of control bullets greater than one can be used in the methods of the present invention for gun identifiability and/or bullet-to-gun classification. Various numbers of evidence bullets can be classified in relation to a suspect gun using the methods of the present invention.